As opposed to explosive diarrhea which is normally cleared in one cataclysmic event, mud butt is characterised by soft stool that may take several attempts before being cleared from one's bowels. Mud butt is an uncomfortable feeling of needing to shit but knowing that there just isn't enough back pressure to deal with the backlog of soft fecal matter.
I had a terrible sleep last night, drank six coffees this morning, and now I have a bad case of mud butt.